Multivariate tail conditional expectation for elliptical distributions

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In this paper we introduce a novel type of a multivariate tail conditional expectation (MTCE) risk measure and explore its properties. We derive an explicit closed-form expression for this risk measure for the elliptical family of distributions taking into account its variance–covariance dependency structure. As a special case we consider the normal, Student-t and Laplace distributions, important and popular in actuarial science and finance. The motivation behind taking the multivariate TCE for the elliptical family comes from the fact that unlike the traditional tail conditional expectation, the MTCE measure takes into account the covariation between dependent risks, which is the case when we are dealing with real data of losses. We illustrate our results using numerical examples in the case of normal and Student-t distributions.

Original languageEnglish
Pages (from-to)216-223
Number of pages8
JournalInsurance: Mathematics and Economics
StatePublished - 1 Sep 2016

Bibliographical note

Publisher Copyright:
© 2016 Elsevier B.V.


  • Cumulative generator
  • Elliptical distributions
  • Multivariate risk measures
  • Positive homogeneity
  • Semi-subadditivity
  • Tail conditional expectation

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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